As a postgraduate student of economics I've been trying to expand my mathematical "toolset". While doing so I've talked to engineers, physicists and mathematicians, many of which have disdained the use of mathematics in economics. Their arguments vary, but one common theme is summed up by mathematician Michael Edesess' critique:
Economics pretends to be mathematics, but it is not mathematics. There is a major difference. No mathematician uses a term in a formula, or a statement of a theorem, unless that term has first been defined with excruciating precision.
And while economists may think they’ve defined terms like "aggregate demand" or "economic growth", they should try reading some real mathematics to see what a precise definition truly is. The economists, I think, leave the work of definition to be inferred from the way the terms are used in the formulas.
I believe I know the precise definition of (quite a few) economic terms, but maybe Edesess is pointing out to some more profound mathematical foundations which I may not be familiar. Could someone expand on his argument and maybe even counter back?